1. Field of the Invention
The present invention relates to a plant control system which operates according to a sliding mode control process.
2. Description of the Prior Art
It is desirable from the standpoint of environmental protection that systems for purifying an exhaust gas emitted from internal combustion engines on automobiles, for example, with a catalytic converter such as a three-way catalytic converter and discharging a purified exhaust gas control the air-fuel ratio of an exhaust gas emitted from an internal combustion engine and introduced into the catalytic converter at an appropriate air-fuel ratio which allows the catalytic converter to have a better ability to purify an exhaust gas. The air-fuel ratio of the exhaust gas is more accurately the ratio of air to fuel in an air-fuel mixture which generates the exhaust gas when combusted.
One conventional air-fuel ratio control system combined with an internal combustion engine has been disclosed in Japanese laid-open patent publication No. 5-321721 which corresponds to U.S. Pat. No. 5,426,935.
The disclosed air-fuel ratio control system has an exhaust gas sensor (O.sub.2 sensor) disposed downstream of a catalytic converter for detecting the concentration of oxygen contained in an exhaust gas which has passed through the catalytic converter. The air-fuel ratio control system determines a target air-fuel ratio for the exhaust gas upstream of the catalytic converter according to a PID (proportional plus integral plus derivative) control process such that the oxygen concentration detected by the exhaust gas sensor will be of a predetermined target value. The air-fuel ratio control system then controls the internal combustion engine according to the target air-fuel ratio thereby to place the air-fuel ratio of the exhaust gas introduced into the catalytic converter (the air-fuel ratio of the air-fuel mixture to be combusted by the internal combustion engine) within a given range or window which enables the catalytic converter to have a good purifying ability.
In the above conventional air-fuel ratio control system, the exhaust system, including the catalytic converter, which ranges from a position upstream of the catalytic converter to a position downstream of the catalytic converter may be considered to be a plant for generating and emitting an exhaust gas having an oxygen concentration detected by the exhaust gas sensor, from an exhaust gas having a certain air-fuel ratio. The internal combustion engine may be considered to be an actuator for generating and emitting an exhaust gas having an air-fuel ratio to be supplied to the plant. Thus, the air-fuel ratio control system may be expressed as a system for determining a target input for the plant (more generally, a manipulated variable which defines an input to the plant) such that an output from the exhaust gas sensor (an oxygen concentration of the exhaust gas) as an output from the plant will be equalized to a given target value, and controlling an output of the internal combustion engine (=an input to the plant) as the actuator according to the target input.
As a result of various studies made by the inventors, it has been found that in order to keep the catalytic converter maximally effective to purify the exhaust gas regardless of aging thereof, it is necessary to adjust the output of an exhaust gas sensor disposed downstream of the catalytic converter to a predetermined target value (constant value) with high accuracy. In the above conventional air-fuel ratio control system based on the PID control process, it is difficult to adjust the output of the exhaust gas sensor disposed downstream of the catalytic converter highly accurately to the given target value (constant value) because of disturbances and a dead time present in the exhaust system of the internal combustion engine.
The inventors have devised a control system for controlling the air-fuel ratio of an exhaust gas introduced into the catalytic converter according to a sliding mode control process (see, for example, U.S. patent application Ser. No. 08/833,091 (Japanese laid-open patent publication No. 9-324681)).
The sliding mode control process is a variable-structure feedback control process. According to the sliding mode control process, a plurailty of state quantities of an object to be controlled are converged onto a hyperplane which is defined by a linear function whose variables are represented by the state quantities, and while the state quantities are being converged onto the hyperplane, the state quantities are converged toward a balanced point (each of the state quantities agrees with its own target value) on the hyperplane. The sliding mode control process is capable of converging the state quantities toward the balanced point on the hyperplane highly stably, without being affected by disturbances, once the state quantities are converged onto the hyperplane.
In a control system devised by the inventors which operates according to the sliding mode control process, the exhaust system of an internal combustion engine which ranges from a position upstream of the catalytic converter to a position downstream of the catalytic converter is modeled as an object to be controlled by the sliding mode control process, in the form of a continuous system (specifically, a continuous time system). Based on the continuous system model, there is established a hyperplane for the sliding mode control process, with two state quantities to be controlled being the output of an exhaust gas sensor disposed downstream of the catalytic converter and a rate of change of the output of the exhaust gas sensor. A balanced point on the hyperplane is a point where the output of the exhaust gas sensor and its rate of change become a predetermined target value and "0", respectively. A target air-fuel ratio for the exhaust gas upstream of the catalytic converter is determined according to the control law of the sliding mode control process for converging the two state quantities (the output of the exhaust gas sensor and its rate of change) toward the balanced point, and the internal combustion engine is controlled according to the determined target air-fuel ratio.
The above control system makes it possible to adjust the output of the exhaust gas sensor disposed downstream of the catalytic converter stably to the predetermined target value based on the characteristics of the sliding mode control process, and hence to maintain desired purifying performance stably for the catalytic converter.
However, since the control system employs the output of the exhaust gas sensor and its rate of change as the state quantities to be controlled by the sliding mode control process, it is necessary to calculate the rate of change of the output of the exhaust gas sensor sequentially.
Furthermore, since the exhaust system to be controlled according to the sliding mode control process is modeled as a continuous system, an algorithm for the processing operation of the sliding mode control process is constructed on the continuous system model. However, because a computer for executing the algorithm can only perform discrete-time processing, it is tedious and time-consuming for the computer to perform the processing operation of the sliding mode control process, in addition to the disadvantage resulting from the sequential calculation of the rate of change of the output of the exhaust gas sensor.
Furthermore, it is difficult to set parameters, including gain coefficients, of the continues system model in a manner to match various operating conditions of the exhaust system, and hence to model the exhaust system with accuracy. According to the sliding mode control process, once the state quantities are converged onto the hyperplane, a certain modeling error can be absorbed together with disturbances. Before the state quantities are converged onto the hyperplane, however, the modeling error tends to adversely affect the convergence of the state quantities onto the hyperplane.
The above drawbacks are not limited to the above air-fuel ratio control system, but may also occur when a plant is modeled as a continuous system and controlled according to the sliding mode control process to equalize an output of the plant to a target value, with the output of the plant and its rate of change being used as state quantities to be controlled by the sliding mode control process.